TSTP Solution File: NUM514+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM514+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:10:11 EDT 2022
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 22
% Syntax : Number of formulae : 49 ( 11 unt; 9 typ; 0 def)
% Number of atoms : 133 ( 61 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 154 ( 72 ~; 30 |; 36 &)
% ( 14 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 9 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 29 ( 11 !; 15 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(sdtsldt0_type,type,
sdtsldt0: ( $i * $i ) > $i ).
tff(xr_type,type,
xr: $i ).
tff(xp_type,type,
xp: $i ).
tff(xm_type,type,
xm: $i ).
tff(xn_type,type,
xn: $i ).
tff(xk_type,type,
xk: $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(doDivides0_type,type,
doDivides0: ( $i * $i ) > $o ).
tff(1,plain,
( ( sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) )
<=> ( sdtasdt0(xp,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) )
<=> ( sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
( aNaturalNumber0(sdtsldt0(xk,xr))
& ( xk = sdtasdt0(xr,sdtsldt0(xk,xr)) )
& aNaturalNumber0(sdtsldt0(xn,xr))
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
& ( sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2613) ).
tff(4,plain,
sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm),
inference(modus_ponens,[status(thm)],[4,2]) ).
tff(6,plain,
sdtasdt0(xp,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtasdt0(sdtsldt0(xn,xr),xm),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)),
inference(symmetry,[status(thm)],[6]) ).
tff(8,plain,
^ [W0: $i] :
refl(
( ( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) )
<=> ~ ( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) ) )),
( ~ ( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) )
<=> ~ ~ ( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) ) )),
rewrite(
( ~ ~ ( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) ) )),
( ~ ( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [W0: $i] :
~ ( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) )
<=> ~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
( ~ ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr)) ) )
=> ( ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) )
| doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) ) )
<=> ~ ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) )
| ~ ( aNaturalNumber0(sdtsldt0(xn,xr))
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
~ ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr)) ) )
=> ( ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) )
| doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(15,plain,
~ ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) )
| ~ ( aNaturalNumber0(sdtsldt0(xn,xr))
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr)) ) ) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) ),
inference(or_elim,[status(thm)],[15]) ).
tff(17,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) ),
inference(modus_ponens,[status(thm)],[17,12]) ).
tff(19,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) ),
inference(modus_ponens,[status(thm)],[18,12]) ).
tff(20,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) ),
inference(modus_ponens,[status(thm)],[19,12]) ).
tff(21,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) ),
inference(modus_ponens,[status(thm)],[20,12]) ).
tff(22,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) ),
inference(modus_ponens,[status(thm)],[21,12]) ).
tff(23,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) ),
inference(modus_ponens,[status(thm)],[22,12]) ).
tff(24,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) ),
inference(modus_ponens,[status(thm)],[23,12]) ).
tff(25,plain,
^ [W0: $i] :
refl(
$oeq(
~ ( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) ),
~ ( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) ))),
inference(bind,[status(th)],]) ).
tff(26,plain,
! [W0: $i] :
~ ( aNaturalNumber0(W0)
& ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) ),
inference(nnf-neg,[status(sab)],[24,25]) ).
tff(27,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) ),
inference(modus_ponens,[status(thm)],[26,11]) ).
tff(28,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) ),
inference(modus_ponens,[status(thm)],[27,9]) ).
tff(29,plain,
( aNaturalNumber0(sdtsldt0(xk,xr))
<=> aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( aNaturalNumber0(sdtsldt0(xk,xr))
<=> aNaturalNumber0(sdtsldt0(xk,xr)) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( aNaturalNumber0(sdtsldt0(xk,xr))
& ( xk = sdtasdt0(xr,sdtsldt0(xk,xr)) )
& aNaturalNumber0(sdtsldt0(xn,xr))
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr)) ) ),
inference(and_elim,[status(thm)],[3]) ).
tff(32,plain,
( aNaturalNumber0(sdtsldt0(xk,xr))
& ( xk = sdtasdt0(xr,sdtsldt0(xk,xr)) )
& aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(and_elim,[status(thm)],[31]) ).
tff(33,plain,
( aNaturalNumber0(sdtsldt0(xk,xr))
& ( xk = sdtasdt0(xr,sdtsldt0(xk,xr)) ) ),
inference(and_elim,[status(thm)],[32]) ).
tff(34,plain,
aNaturalNumber0(sdtsldt0(xk,xr)),
inference(and_elim,[status(thm)],[33]) ).
tff(35,plain,
aNaturalNumber0(sdtsldt0(xk,xr)),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)),
inference(modus_ponens,[status(thm)],[35,29]) ).
tff(37,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) )
| ~ aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) )
| ~ aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) )
| ~ aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0) ) )
| ~ aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
$false,
inference(unit_resolution,[status(thm)],[39,36,28,7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM514+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.32 % Computer : n009.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Sep 2 11:18:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------